Zakhar Kabluchko

activity

20122026

most citedRandom determinants, mixed volumes of ellipsoids, and zeros of Gaussian random fields

1 citations · 1 across the 22 of their papers we have counts for

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9 papers · 2 filters

math.PR2025

Zeros of polynomial powers under the heat flow

Antonia Höfert, Jonas Jalowy, Zakhar Kabluchko

We study the zero evolution of high powers of polynomials under the heat flow. For any fixed polynomial $P (z)$ , we prove that the empirical zero distribution of its heat-evolved $n…

math.PR2025

On the distribution patterns of zeros for random polynomials with regularly varying coefficients

Zakhar Kabluchko, Boris Khoruzhenko, Alexander Marynych

This paper investigates asymptotic distribution of complex zeros of random polynomials $P_{n} (z) := \sum_{k = 0}^{n} b (k) ξ_{k} z^{k}$ , as $n \to \infty$ , where $b$ is a regularly varying functi…

math.PR2025

Zero distribution of multiplicative Hermite and Laguerre polynomials

Zakhar Kabluchko

It is well-known that, as $n \to \infty$ , the zero distribution of the $n$ -th Hermite polynomial converges to the semicircular law (the free normal distribution), while the zero dist…

math.PR2025

On the shape of the typical Poisson-Voronoi cell in high dimensions

Matthias Irlbeck, Zakhar Kabluchko, Tobias Müller

We study the typical cell of the Poisson-Voronoi tessellation. We show that when divided by the $d$ -th root of the intensity parameter $λ$ of the Poisson process times the volume o…

math.PR2025

Zeros and exponential profiles of polynomials I: Limit distributions, finite free convolutions and repeated differentiation

Jonas Jalowy, Zakhar Kabluchko, Alexander Marynych

Given a sequence of polynomials $(P_{n})_{n \in N}$ with only nonpositive zeros, the aim of this article is to present a user-friendly approach for determining the limiting…

math.PR2025

Beta Polytopes and Beta Cones: An Exactly Solvable Model in Geometric Probability

Zakhar Kabluchko, David Albert Steigenberger

Let $X_{1}, \dots, X_{n}$ be independent random points in the unit ball of $R^{d}$ such that $X_{i}$ follows a beta distribution with the density proportional to $(1-\|x\|^2)^{β_i}…

math.PR2025

Almost periodic stochastic processes with applications to analytic number theory

Alexander Iksanov, Zakhar Kabluchko, Alexander Marynych

A classical fact of the theory of almost periodic functions is the existence of their asymptotic distributions. In probabilistic terms, this means that if $f$ is a Besicovitch almo…

math.PR2025

A refinement of the Sylvester problem: Probabilities of combinatorial types

Zakhar Kabluchko, Hugo Panzo

Let $X_{1}, \dots, X_{d + 2}$ be random points in $R^{d}$ . The classical Sylvester problem asks to determine the probability that the convex hull of these points, denoted by $P:=…

math.PR2025

Sylvester's problem for beta-type distributions

Anna Gusakova, Zakhar Kabluchko

Consider $d + 2$ i.i.d. random points $X_{1}, \dots, X_{d + 2}$ in $R^{d}$ . In this note, we compute the probability that their convex hull is a simplex focusing on three specific…